bibkey: doumas2025fibonacciredheffer authors: Aristides V. Doumas; Panayiotis J. Psarrakos year: 2025 title: The Fibonacci–Redheffer Matrix and its Properties doi: null url: https://arxiv.org/abs/2511.13627v3 claim: The preprint studies a Redheffer matrix weighted by Fibonacci entries, with determinant equal to a Fibonacci factorial times a truncated Mobius sum; it does not supply a Robin estimate or an RH proof. strata_touched: [] license: citation-only triage: anchor

The Fibonacci–Redheffer matrix

The inspected source is arXiv:2511.13627v3, submitted 17 November 2025 and revised 27 September 2026. The statements below are attributed to that version; the proof and numerical asymptotics were not independently audited here, and no Lean verification is claimed.

For $n\ge 3$, the source defines a matrix with Redheffer divisibility support and Fibonacci weight $F_i$ on the entry in row $i$ whenever $i\mid j$. Its determinant is

$$\det (FR(n))=\left(\prod _{j=1}^n{F}_j\right)\sum _{k=1}^n\frac{\mu (k)}{F_k}.$$

The paper proves that the displayed partial sums are negative for $n\ge 3$ and converge rapidly to a negative constant. More generally, for a positive weight sequence $(a_j)$, Theorem 21 gives the determinant factor $1+{\sum }_{k=2}^n\mu (k)/a_k$. It equals ${\sum }_{k=1}^n\mu (k)/a_k$ when $a_1=1$, as in the Fibonacci specialization; the general statement does not assume that normalization.

Boundary for the FIB–Robin route

This is a genuine historical intersection of Fibonacci weights, divisibility support, and the Möbius function. It is a finite matrix identity, however, and its convergent weight $1/F_k$ is not the Robin weight $1/k$ or the complete divisor average $\sigma (N)/N$. The source gives no map from a five-window FIB address or from $N_g=1+F_{r}g$ to the matrix index $n$ that would preserve the required prime-power coefficients. It therefore cannot be used as a Robin upper bound, a signed FIB residual estimate, or a proof of RH without a new coefficient-preserving bridge.

The reusable interface is the determinant factorization: a Fibonacci-weighted divisibility operator can expose a truncated Möbius transform. Any proposed spectral FIB argument should state how that transform relates to the ordinary Möbius/Robin transform before importing conclusions from this source.